ksharma12 wrote:

A set consist of 2n-1 element. What is the number of subsets of this set which contain at most n-1 elements?

A. 2^(2n-2)

B. 2^(2n) - 2

C. 2^(2n) -1

D. 2^(2n)

E. 2^(2n-1)

I dont really know what this question is asking. I dont know the reasoning or the idea behind an empty subset. Can someone explain this question and answer as if they were explaining it to a beginner? Thank you.

Yes answer is A indeed. Please allow me to show my procedure

I used n=3, so then we have

5!/2!3! + 5!/4!1! + 5!/0!5!

10 + 5 + 1 = 16

So our target is 16

Now replace in answer choices

A gives us 2^4 = 16

Hence A is the correct option

Read carefully it says at most so keep in mind that picking a small number such as 3 will help you save time since you have to list fewer outcomes

Avoid 2 since you will get 1 arrangement (n-1) and may be risky since 1 is a number with certain unique properties

Hope all of this helps

If it does, gimme some Kudos

Cheers!

J